Quantum simulator

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In this photograph of a quantum simulator crystal the ions are fluorescing, indicating the qubits are all in the same state (either "1" or "0"). Under the right experimental conditions, the ion crystal spontaneously forms this nearly perfect triangular lattice structure. Credit: Britton/NIST Quantum Simulator Crystal.jpg
In this photograph of a quantum simulator crystal the ions are fluorescing, indicating the qubits are all in the same state (either "1" or "0"). Under the right experimental conditions, the ion crystal spontaneously forms this nearly perfect triangular lattice structure. Credit: Britton/NIST
Trapped ion quantum simulator illustration: The heart of the simulator is a two-dimensional crystal of beryllium ions (blue spheres in the graphic); the outermost electron of each ion is a quantum bit (qubit, red arrows). The ions are confined by a large magnetic field in a device called a Penning trap (not shown). Inside the trap the crystal rotates clockwise. Credit: Britton/NIST Quantum Simulator Illustration (150 dpi).jpg
Trapped ion quantum simulator illustration: The heart of the simulator is a two-dimensional crystal of beryllium ions (blue spheres in the graphic); the outermost electron of each ion is a quantum bit (qubit, red arrows). The ions are confined by a large magnetic field in a device called a Penning trap (not shown). Inside the trap the crystal rotates clockwise. Credit: Britton/NIST

Quantum simulators permit the study of a quantum system in a programmable fashion. In this instance, simulators are special purpose devices designed to provide insight about specific physics problems. [1] [2] [3] Quantum simulators may be contrasted with generally programmable "digital" quantum computers, which would be capable of solving a wider class of quantum problems.

Contents

A universal quantum simulator is a quantum computer proposed by Yuri Manin in 1980 [4] and Richard Feynman in 1982. [5]

A quantum system may be simulated by either a Turing machine or a quantum Turing machine, as a classical Turing machine is able to simulate a universal quantum computer (and therefore any simpler quantum simulator), meaning they are equivalent from the point of view of computability theory. The simulation of a quantum physics by a classical computer has been shown to be inefficient. [6] In other words, quantum computers provide no additional power over classical computers in terms of computability, but it is suspected that they can solve certain problems faster than classical computers, meaning they may be in different complexity classes, which is why quantum Turing machines are useful for simulating quantum systems. This is known as quantum supremacy, the idea that there are problems only quantum Turing machines can solve in any feasible amount of time.

A quantum system of many particles could be simulated by a quantum computer using a number of quantum bits similar to the number of particles in the original system. [5] This has been extended to much larger classes of quantum systems. [7] [8] [9] [10]

Quantum simulators have been realized on a number of experimental platforms, including systems of ultracold quantum gases, polar molecules, trapped ions, photonic systems, quantum dots, and superconducting circuits. [11]

Solving physics problems

Many important problems in physics, especially low-temperature physics and many-body physics, remain poorly understood because the underlying quantum mechanics is vastly complex. Conventional computers, including supercomputers, are inadequate for simulating quantum systems with as few as 30 particles because the dimension of the Hilbert space grows exponentially with particle number. [12] Better computational tools are needed to understand and rationally design materials whose properties are believed to depend on the collective quantum behavior of hundreds of particles. [2] [3] Quantum simulators provide an alternative route to understanding the properties of these systems. These simulators create clean realizations of specific systems of interest, which allows precise realizations of their properties. Precise control over and broad tunability of parameters of the system allows the influence of various parameters to be cleanly disentangled.

Quantum simulators can solve problems which are difficult to simulate on classical computers because they directly exploit quantum properties of real particles. In particular, they exploit a property of quantum mechanics called superposition, wherein a quantum particle is made to be in two distinct states at the same time, for example, aligned and anti-aligned with an external magnetic field. Crucially, simulators also take advantage of a second quantum property called entanglement, allowing the behavior of even physically well separated particles to be correlated. [2] [3] [13]

Recently quantum simulators have been used to obtain time crystals [14] [15] and quantum spin liquids. [16] [17]

Trapped-ion simulators

Ion trap based system forms an ideal setting for simulating interactions in quantum spin models. [18] A trapped-ion simulator, built by a team that included the NIST can engineer and control interactions among hundreds of quantum bits (qubits). [19] Previous endeavors were unable to go beyond 30 quantum bits. The capability of this simulator is 10 times more than previous devices. It has passed a series of important benchmarking tests that indicate a capability to solve problems in material science that are impossible to model on conventional computers.

The trapped-ion simulator consists of a tiny, single-plane crystal of hundreds of beryllium ions, less than 1 millimeter in diameter, hovering inside a device called a Penning trap. The outermost electron of each ion acts as a tiny quantum magnet and is used as a qubit, the quantum equivalent of a “1” or a “0” in a conventional computer. In the benchmarking experiment, physicists used laser beams to cool the ions to near absolute zero. Carefully timed microwave and laser pulses then caused the qubits to interact, mimicking the quantum behavior of materials otherwise very difficult to study in the laboratory. Although the two systems may outwardly appear dissimilar, their behavior is engineered to be mathematically identical. In this way, simulators allow researchers to vary parameters that couldn’t be changed in natural solids, such as atomic lattice spacing and geometry.

Friedenauer et al., adiabatically manipulated 2 spins, showing their separation into ferromagnetic and antiferromagnetic states. [20] Kim et al., extended the trapped ion quantum simulator to 3 spins, with global antiferromagnetic Ising interactions featuring frustration and showing the link between frustration and entanglement [21] and Islam et al., used adiabatic quantum simulation to demonstrate the sharpening of a phase transition between paramagnetic and ferromagnetic ordering as the number of spins increased from 2 to 9. [22] Barreiro et al. created a digital quantum simulator of interacting spins with up to 5 trapped ions by coupling to an open reservoir [23] and Lanyon et al. demonstrated digital quantum simulation with up to 6 ions. [24] Islam, et al., demonstrated adiabatic quantum simulation of the transverse Ising model with variable (long) range interactions with up to 18 trapped ion spins, showing control of the level of spin frustration by adjusting the antiferromagnetic interaction range. [25] Britton, et al. from NIST has experimentally benchmarked Ising interactions in a system of hundreds of qubits for studies of quantum magnetism. [19] Pagano, et al., reported a new cryogenic ion trapping system designed for long time storage of large ion chains demonstrating coherent one and two-qubit operations for chains of up to 44 ions. [26] Joshi, et al., probed the quantum dynamics of 51 individually controlled ions, realizing a long-range interacting spin chain. [27]

Ultracold atom simulators

Many ultracold atom experiments are examples of quantum simulators. These include experiments studying bosons or fermions in optical lattices, the unitary Fermi gas, Rydberg atom arrays in optical tweezers. A common thread for these experiments is the capability of realizing generic Hamiltonians, such as the Hubbard or transverse-field Ising Hamiltonian. Major aims of these experiments include identifying low-temperature phases or tracking out-of-equilibrium dynamics for various models, problems which are theoretically and numerically intractable. [28] [29] Other experiments have realized condensed matter models in regimes which are difficult or impossible to realize with conventional materials, such as the Haldane model and the Harper-Hofstadter model. [30] [31] [32] [33] [34]

Superconducting qubits

Quantum simulators using superconducting qubits fall into two main categories. First, so called quantum annealers determine ground states of certain Hamiltonians after an adiabatic ramp. This approach is sometimes called adiabatic quantum computing. Second, many systems emulate specific Hamiltonians and study their ground state properties, quantum phase transitions, or time dynamics. [35] Several important recent results include the realization of a Mott insulator in a driven-dissipative Bose-Hubbard system and studies of phase transitions in lattices of superconducting resonators coupled to qubits. [36] [37]

See also

Related Research Articles

<span class="mw-page-title-main">Quantum computing</span> Technology that uses quantum mechanics

A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior using specialized hardware. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer. In particular, a large-scale quantum computer could break widely used encryption schemes and aid physicists in performing physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications.

This is a timeline of quantum computing.

<span class="mw-page-title-main">Trapped-ion quantum computer</span> Proposed quantum computer implementation

A trapped-ion quantum computer is one proposed approach to a large-scale quantum computer. Ions, or charged atomic particles, can be confined and suspended in free space using electromagnetic fields. Qubits are stored in stable electronic states of each ion, and quantum information can be transferred through the collective quantized motion of the ions in a shared trap. Lasers are applied to induce coupling between the qubit states or coupling between the internal qubit states and the external motional states.

<span class="mw-page-title-main">Optical lattice</span> Atomic-scale structure formed through the Stark shift by opposing beams of light

An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate at the potential extrema. The resulting arrangement of trapped atoms resembles a crystal lattice and can be used for quantum simulation.

<span class="mw-page-title-main">Nuclear magnetic resonance quantum computer</span> Proposed spin-based quantum computer implementation

Nuclear magnetic resonance quantum computing (NMRQC) is one of the several proposed approaches for constructing a quantum computer, that uses the spin states of nuclei within molecules as qubits. The quantum states are probed through the nuclear magnetic resonances, allowing the system to be implemented as a variation of nuclear magnetic resonance spectroscopy. NMR differs from other implementations of quantum computers in that it uses an ensemble of systems, in this case molecules, rather than a single pure state.

Quantum annealing (QA) is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions, by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete with many local minima; such as finding the ground state of a spin glass or the traveling salesman problem. The term "quantum annealing" was first proposed in 1988 by B. Apolloni, N. Cesa Bianchi and D. De Falco as a quantum-inspired classical algorithm. It was formulated in its present form by T. Kadowaki and H. Nishimori in 1998 though an imaginary-time variant without quantum coherence had been discussed by A. B. Finnila, M. A. Gomez, C. Sebenik and J. D. Doll in 1994.

In condensed matter physics, an ultracold atom is an atom with a temperature near absolute zero. At such temperatures, an atom's quantum-mechanical properties become important.

A quantum bus is a device which can be used to store or transfer information between independent qubits in a quantum computer, or combine two qubits into a superposition. It is the quantum analog of a classical bus.

Adiabatic quantum computation (AQC) is a form of quantum computing which relies on the adiabatic theorem to perform calculations and is closely related to quantum annealing.

The toric code is a topological quantum error correcting code, and an example of a stabilizer code, defined on a two-dimensional spin lattice. It is the simplest and most well studied of the quantum double models. It is also the simplest example of topological order—Z2 topological order (first studied in the context of Z2 spin liquid in 1991). The toric code can also be considered to be a Z2 lattice gauge theory in a particular limit. It was introduced by Alexei Kitaev.

<span class="mw-page-title-main">Time crystal</span> Structure that repeats in time; a novel type or phase of non-equilibrium matter

In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. The system cannot lose energy to the environment and come to rest because it is already in its quantum ground state. Time crystals were first proposed theoretically by Frank Wilczek in 2012 as a time-based analogue to common crystals – whereas the atoms in crystals are arranged periodically in space, the atoms in a time crystal are arranged periodically in both space and time. Several different groups have demonstrated matter with stable periodic evolution in systems that are periodically driven. In terms of practical use, time crystals may one day be used as quantum computer memory.

<span class="mw-page-title-main">Christopher Monroe</span> American physicist

Christopher Roy Monroe is an American physicist and engineer in the areas of atomic, molecular, and optical physics and quantum information science, especially quantum computing. He directs one of the leading research and development efforts in ion trap quantum computing. Monroe is the Gilhuly Family Presidential Distinguished Professor of Electrical and Computer Engineering and Physics at Duke University and is College Park Professor of Physics at the University of Maryland and Fellow of the Joint Quantum Institute and Joint Center for Quantum Computer Science. He is also co-founder of IonQ, Inc.

In quantum computing, a qubit is a unit of information analogous to a bit in classical computing, but it is affected by quantum mechanical properties such as superposition and entanglement which allow qubits to be in some ways more powerful than classical bits for some tasks. Qubits are used in quantum circuits and quantum algorithms composed of quantum logic gates to solve computational problems, where they are used for input/output and intermediate computations.

Shortcuts to adiabaticity (STA) are fast control protocols to drive the dynamics of system without relying on the adiabatic theorem. The concept of STA was introduced in a 2010 paper by Xi Chen et al. Their design can be achieved using a variety of techniques. A universal approach is provided by counterdiabatic driving, also known as transitionless quantum driving. Motivated by one of authors systematic study of dissipative Landau-Zener transition, the key idea was demonstrated earlier by a group of scientists from China, Greece and USA in 2000, as steering an eigenstate to destination. Counterdiabatic driving has been demonstrated in the laboratory using a time-dependent quantum oscillator.

Adolfo del Campo is a Spanish physicist and a professor of physics at the University of Luxembourg. He is best known for his work in quantum control and theoretical physics. He is notable as one of the pioneers of shortcuts to adiabaticity. He was elected as a Fellow of the American Physical Society in 2023.

Hamiltonian simulation is a problem in quantum information science that attempts to find the computational complexity and quantum algorithms needed for simulating quantum systems. Hamiltonian simulation is a problem that demands algorithms which implement the evolution of a quantum state efficiently. The Hamiltonian simulation problem was proposed by Richard Feynman in 1982, where he proposed a quantum computer as a possible solution since the simulation of general Hamiltonians seem to grow exponentially with respect to the system size.

This glossary of quantum computing is a list of definitions of terms and concepts used in quantum computing, its sub-disciplines, and related fields.

Quantum computational chemistry is an emerging field that exploits quantum computing to simulate chemical systems. Despite quantum mechanics' foundational role in understanding chemical behaviors, traditional computational approaches face significant challenges, largely due to the complexity and computational intensity of quantum mechanical equations. This complexity arises from the exponential growth of a quantum system's wave function with each added particle, making exact simulations on classical computers inefficient.

References

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